
Talk about patterns in the mathematics classroom
Roubíček, Filip
The poster deals with the talk in the mathematics classroom which is focused on looking for relationships in a pattern. The communication of students is observed in the environment of geometrical patterns in a triangle grid and their transformation into arithmetic patterns or algebraic functions. It shows how pupils/students reason about relationships in these patterns and among these patterns, how they describe and express their generalizations in words or symbols.

 

Heuristic strategies of mathematical problem solving on lower secondary school
Přibyl, Jiří ; Roubíček, Filip (advisor) ; Jančařík, Antonín (referee) ; Odvárko, Oldřich (referee)
The dissertation thesis deals with mathematical problemsolving at lower secon dary level, as viewed from the perspective of heuristic strategies. The aim of the thesis is to comprehensibly summarize the results of research which began in 2012 and runs until now. The results concern both with theoretical and empirical parts of our research. This research study was conducted in fifteen lower secondary and upper secondary classes. Three dimensional classification of use of heuristic strategies and the structure of heuristic strategies' characteristics were developed by the author, and these constructs are presented in this work. The theory of mathematical problem and mathematical problem solving method is an integral part of this thesis too. Furthermore, the author presents a summary of all strategies used in the experiments; each strategy is fully described and illustrated by an appropriate example. The results of several shortterm research studies (three months) and a longitudinal research study (sixteen months) are analysed in the empirical part of the thesis. This part also strives to find answers to several research questions, e.g.: " Could certain strategies be taught in a shortterm period (three months)?", " Which strategies are suitable for an average pupil?" or " Are the pupils able to...

 

Transfer between verbal and algebraic descriptions. Pupils' strategies and problems
Novotná, Anežka ; Vondrová, Naďa (advisor) ; Roubíček, Filip (referee)
The aim of this thesis is to gain insight into the problems that pupils have when switching between verbal and algebraic expressions, through the analysis of their problemsolving processes. The work is divided into theoretical and experimental parts. The theoretical part of the paper contains three sections. The first describes the analysis of three selected Czech textbooks series for primary schools in terms of teaching the concept of variables and algebraic expressions. The next section deals with international comparative research TIMSS and the success of Czech pupils of year 8 in algebra. In the third section, results of international research concerning the issue of transition between verbal and algebraic expressions are described. The main part of the work is the experimental part, it aims to describe the difficulties encountered by pupils in algebra and to identify their likely sources. The basis for the own research was a set of 9 problems based on released TIMSS problems. The target group of pupils was year 9 of primary school, with whom the investigation was carried out via thinkaloud interviews. First, a pilot study was conducted on a sample of 3 pupils, during which a set of test problems was checked. The main study involved 8 pupils. The thinkaloud interviews were recorded and later...

 

Pupils' Communication when Solving Problems in Mathematics in Groups
Čmejrková, Kamila ; Sýkora, Václav (advisor) ; Půlpán, Zdeněk (referee) ; Roubíček, Filip (referee)
Cooperative group work presents further tasks for students in addition to solving the assigned problems themselves. The students are forced to formulate their suggestions and approaches and defend, substantiate and explain them to their partners more than when they are working independently. When working cooperatively, the students create and reconstruct their relationships to one another. Cooperation in a group can give the students room to acquire new skills not only in the area of mathematics, but also in the area of interpersonal communication and social relationships. The aim of this thesis is to identify features which are characteristic for communication in the cooperative solving of problems and to determine whether communication in the group influences the process of problemsolving, and if so, how. The basis for the analysis was a corpus of transcripts of conversations between students which took place as part of an experiment. In this experiment, elementary school students of homogeneous ability between the ages of 13 and 15 worked on solving logic problems in small groups. The students' task was to solve an assigned set of problems and to explain their ideas and approaches to each other in such a way that every member of the group could understand the process leading to the achieved solution. In...


Origami as didacktical environment in matematical education
Boháčová, Jana ; Roubíček, Filip (advisor) ; Vondrová, Naďa (referee)
The thesis deals with origami as a learning environment in mathematics education. The two main aims of the thesis are to show the possibilities of using origami in various areas of mathematics teaching and learning, especially in synthetic geometry and calculations in geometry, and to suggest specific origamibased activities for secondary education. First, origami is introduced in its historical context and its geometrical axioms are described. Further, advantages and difficulties of using origami in mathematics education are discussed, with respect to the type and level of school. The fundamental part of the thesis consists of description and didactical analysis of tasks based on folding of an equilateral triangle and various polyhedra. Some of these tasks are adapted from other resources, some were designed by the author. Based on direct experience with employing origamibased tasks in different classrooms, methodological recommendations are added to the individual analyses, facilitating the practical usage of the thesis.


Origami as a Learning Environment in Mathematics Education
Boháčová, Jana ; Vondrová, Naďa (referee) ; Roubíček, Filip (advisor)
The thesis deals with origami as a learning environment in mathematics education. The two main aims of the thesis are to show the possibilities of using origami in various areas of mathematics teaching and learning, especially in synthetic geometry and calculations in geometry, and to suggest specific origamibased activities for secondary education. First, origami is introduced in its historical context and its geometrical axioms are described. Further, advantages and difficulties of using origami in mathematics education are discussed, with respect to the type and level of school. The fundamental part of the thesis consists of description and didactical analysis of tasks based on folding of an equilateral triangle and various polyhedra. Some of these tasks are adapted from other resources, some were designed by the author. Based on direct experience with employing origamibased tasks in different classrooms, methodological recommendations are added to the individual analyses, facilitating the practical usage of the thesis.


Several New Methods for Developing Geometric Visualization
Hašková, Lenka ; Sýkora, Václav (advisor) ; Roubíček, Filip (referee)
'Často se setkáváme s názorem, že geometrické učivo je ve školské matematice podceňováno, a to nejen z hlediska jeho rozsahu v osnovách nebo vzdělávacích programech. Šetření ukazují, že i učitelé dávají ve své práci přednost ostatním partiím matematiky. Tento jev je celosvětový a nemáme pro něj přiměřené zdůvodnění. Přitom je v rozporu se základním posláním matematického vzdělání. Školská matematika vytváří předpoklady pro rozvoj řady kompetencí nezbytných pro každého člověka v jeho praktickém životě. Geometrizace reálného světa, orientace v prostoru a času, dovednosti modelovat a zobrazovat, to jsou významné a nezpochybnitelné cíle školské geometrie. Říkáme, že každý člověk by měl být vybaven dostatečně rozvinutou geometrickou představivostí. Ta mu usnadňuje celou řadu aktivit důležitých pro jeho úspěšný praktický život. Učitelé matematiky i didaktici proto hledají nové formy rozvíjení této představivosti. V současné době dáváme přednost formám, které žáky pozitivně motivují osvojování geometrických poznatků, mají konstruktivní charakter a na základní škole přispívají také paralelnímu rozvíjení dovedností motorických. Zvolila jsem si geometrii překládaného papíru jako východisko mého úsilí. V souvislosti s ní jsem dospěla i otázkám rozvíjení prostorové představivosti. Ta mě potom dovedla některým novým...
